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The Entrance Times For Circle Maps With A Break, Akhtam Dzhalilov, Javlon Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In present work we study the entrance times for circle homeomorphisms with one break point and universal renormalization properties. Consider the set X of all orientation preserving circle homeomorphisms T with one break point and golden mean rotation number. It is well known that the renormalization group transformation has a unique periodic point T _b with period 2. Denote by B the set of all circle maps C¹ -conjugated to T _b . Consider the map T ∈ B and its unique probability invariant measure μ . Denote by E(x) the first entrance times of x to interval defined …